Question: The sum of two numbers is $41$, and their difference is $11$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 41}$ ${x-y = 11}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 52 $ $ x = \dfrac{52}{2} $ ${x = 26}$ Now that you know ${x = 26}$ , plug it back into $ {x+y = 41}$ to find $y$ ${(26)}{ + y = 41}$ ${y = 15}$ You can also plug ${x = 26}$ into $ {x-y = 11}$ and get the same answer for $y$ ${(26)}{ - y = 11}$ ${y = 15}$ Therefore, the larger number is $26$, and the smaller number is $15$.